Question: Solve for $x$ and $y$ using substitution. ${3x-5y = 6}$ ${x = -y+10}$
Since $x$ has already been solved for, substitute $-y+10$ for $x$ in the first equation. ${3}{(-y+10)}{- 5y = 6}$ Simplify and solve for $y$ $-3y+30 - 5y = 6$ $-8y+30 = 6$ $-8y+30{-30} = 6{-30}$ $-8y = -24$ $\dfrac{-8y}{{-8}} = \dfrac{-24}{{-8}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {x = -y+10}\thinspace$ to find $x$ ${x = -}{(3)}{ + 10}$ $x = -3 + 10$ ${x = 7}$ You can also plug ${y = 3}$ into $\thinspace {3x-5y = 6}\thinspace$ and get the same answer for $x$ : ${3x - 5}{(3)}{= 6}$ ${x = 7}$